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受欢迎的函数 >

extreme f(x)=((x+1))/(x^2+x+1)

解答

极值点

f (x) = \frac{( x + 1 )}{x ^{2} + x + 1}

解答

极小值 (- 2, - \frac{1}{3}), 极大值 (0, 1)

求解步骤

f^{'} (x) = \frac{- x ^{2} - 2 x}{( x ^{2} + x + 1 ) ^{2}}

Find intervals:

递减

: - \infty < x < - 2,

递增

: - 2 < x < 0,

递减

: 0 < x < \infty

将

x = - 2

代入

\frac{x + 1}{x ^{2} + x + 1} : - \frac{1}{3}

极小值 (- 2, - \frac{1}{3})

将

x = 0

代入

\frac{x + 1}{x ^{2} + x + 1} : 1

极大值 (0, 1)

极小值 (- 2, - \frac{1}{3}), 极大值 (0, 1)

作图

流行的例子

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